RPCA (from SIAM OPT 11 conference). This shows how to use TFOCS to perform Robust Principal Component Analysis. For a background on RPCA, see Robust Principal Component Analysis? by J. Candès, X. Li, Y. Ma, and J. Wright, in Journal of ACM58(1), 1-37.

Support Vector Machines (SVM). This covers basic SVM as well as a type of sparse-SVM. For a background in SVM, there are many online resources; a good introduction is chapter 8.6 of the free online textbook Convex Optimization by Stephen Boyd and Lieven Vandenberghe (2004).

Alternating projections. Covers three methods (alternating directions, Dykstra’s projection algorithm, and TFOCS) for projecting a point onto the intersection of two convex sets. For some problems, TFOCS is extremely efficient compared to the alternative methods. Demo added July 17 2012.